exercise3:

             RK3
  K  Y[2.0]  E[K]

0 -3.2704587728350876 0.0002117936381371699
1 -3.2706461297879597 2.4436685267748004e-05
2 -3.2706676318407615 2.9346324659229595e-06
3 -3.2706702069151605 3.5955805710585764e-07
4 -3.270670521975921 4.4497290296874326e-08
5 -3.2706705609388216 5.534435132403814e-09

     RK3
  K  R[K]=E[K]/E[K+1]

0 8.667036294676967
1 8.327000246711481
2 8.16177640279932
3 8.080448375777042
4 8.04007802645389

     RK2    RK3
  K  Error  Error

0 0.004225496198696277 0.0002117936381371699
1 0.0009743485309416933 2.4436685267748004e-05
2 0.00023428761101440543 2.9346324659229595e-06
3 5.746367785031126e-05 3.5955805710585764e-07
4 1.4230623563982192e-05 4.4497290296874326e-08
5 3.5409411949238745e-06 5.534435132403814e-09